The operational characteristics of generators cause non-convexity in the electricity market. The presence of non-convexity implies that market participants will bear lost opportunity costs under linear prices, which motivates them to violate the dispatch decisions or obtain excess profits through strategic bidding. To resolve this issue, finding a reasonable pricing scheme under non-convexity is a research field of great concern. Currently, most studies regard uplift payments as an indicator to quantify the effectiveness of a pricing scheme. It is usually recognized that convex hull pricing is a promising pricing method with nice incentive properties because it minimizes the uplift payment and thus improves market transparency. However, whether the pricing mechanism can guide truthful bidding has not been thoroughly investigated. In this paper, considering the complex market clearing process, we propose a framework with certain qualifications to analyze the incentive properties under different pricing schemes. Then, conclusions regarding the incentive property of different pricing schemes are provided. The effectiveness and correctness of the proposed method are validated using the numerical results of case studies.